TY  - CHAP
Y1  - 2016///
EP  - 111
TI  - Efficient Syntax-Driven Lumping of Differential Equations
PB  - Springer
UR  - http://dx.doi.org/10.1007/978-3-662-49674-9_6
T2  - Tools and Algorithms for the Construction and Analysis of Systems. 22nd International Conference, TACAS 2016
A1  - Cardelli, Luca
A1  - Tribastone, Mirco
A1  - Tschaikowski, Max
A1  - Vandin, Andrea
AV  - public
SN  - 978-3-662-49673-2
SP  - 93
T3  - Lecture Notes in Computer Science
ID  - eprints3437
N2  - We present an algorithm to compute exact aggregations of a class of systems of ordinary differential equations (ODEs). Our approach consists in an extension of Paige and Tarjan?s seminal solution to the coarsest refinement problem by encoding an ODE system into a suitable discrete-state representation. In particular, we consider a simple extension of the syntax of elementary chemical reaction networks because (i) it can express ODEs with derivatives given by polynomials of degree at most two, which are relevant in many applications in natural sciences and engineering; and (ii) we can build on two recently introduced bisimulations, which yield two complementary notions of ODE lumping. Our algorithm computes the largest bisimulations in O(r?s?logs)O(r?s?log?s) time, where r is the number of monomials and s is the number of variables in the ODEs. Numerical experiments on real-world models from biochemistry, electrical engineering, and structural mechanics show that our prototype is able to handle ODEs with millions of variables and monomials, providing significant model reductions.
ER  -